Should homeless people travel south for the winter?

Good luck with that.

It's a long walk, and in many instances, it's illegal to hitchhike on major roadways (where you'd be more likely to be offered a lift).

And then there's people's hesitation to readily welcome into their vehicle another person who is dirty and smelly because they don't have the means to keep themselves up on a regular, consistent basis.

Then there's the sheer distance when you don't have money or a vehicle. If one is leaving Detroit and heading to Miami, that's a long haul, for example. And you forgot the fact that the authorities in Miami will not be out waiting to greet you with food and shelter and assistance, either. They don't want more homeless, migrating or otherwise, because there are plenty of homeless people in Florida (and no, they aren't all "beach bums" here, either) and it's a challenge to provide services to meet needs whether it's though the public sector or the non-profit sector. Florida is broke, and unemployment is high. Homeless migrants would not be received with "open arms" by many here.

While in theory it makes sense to move south for the winter because our ancestors probably did this on a seasonal basis, following sources of food, in today's society? Not so much.